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July, 2005

The Moon Illusion

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The moon illusion – short history of a long-standing mystery of science

When the moon rises over the horizon on a beautiful summer evening, it

looks larger than usual. Perhaps you have observed that in the past couple of

weeks, this interesting summer phenomenon has been particularly prominent.

Although some aspects of the phenomenon are well understood, others are

not and an encompassing explanation is, amazingly, still missing.

For a hyperlinked overview of all issues of "Ulrich's

Bimonthly" and the previous "Picture of the Month" series, see the site map

Previous | Next

The summer, the Sun, and the Moon This year, the summer solstice (June

21) nearly coincided with the full moon (June 22) – ideal for observing the

moon illusion. Since the full moon and the sun are opposite, and since in

summer the sun is high, the full moon in summer is low at the horizon. When

the full moon is near the horizon, we perceive it larger than when it stands

near the zenith. Since June 1987, the full moon hasn't been as low in the sky

as we see it in these weeks; consequently, the moon illusion is currently

stronger than it has been for eighteen years.

In search of an illusion When the moon illusion occurs, the moon looks

some 50% larger than usual. It is a phenomenon that is undoubtedly

occurring, yet cameras, unlike the human eye, cannot see it. It is at the same

time real and unreal, fact and illusion. The circumstance calls for an

explanation, but there is no entirely convincing theory that would explain it.

The two most popular theories actually stand more for research hypotheses

than for well-established findings. They are the "sky dome" (or distance

illusion) theory and the "oculomotor micropsia" (or angular size illusion, a

term to be explained in a moment) theory, but both offer only partial

explanations.

So much we know: our perception of the moon varies with its position above

the horizon, although its linear size (actual physical size as measured by its

diameter and volume) and distance from the earth remain about the same. To

be precise, the distance varies slightly: when we observe the moon at the

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horizon, it is roughly one earth radius further away than at the zenith, which

means its angular size (the angle of regard formed by the endpoints of its

diameter) is a nuance smaller than when it is overhead – just the opposite of

the moon illusion. According to Simanek (2002), the difference in angular

size is 2%; but for our present purpose, it is accurate enough to assume that

the moon's distance from a human observer, and thus its angular size, are

constant.

Angular size, in distinction to linear size, includes information on distance;

the angular size of an object decreases proportionally to its distance, that is,

it is inversely proportional to distance. Since the "true" (undistorted) angular

size of the moon on the surface of the earth is basically constant, there

remain two basic options for explaining the moon illusion:

Either we assume that its perceived angular size (as distinguished from

its actual angular size) varies due to optical distortions, a variation that

could be caused either by the refraction of the moon's light in the

atmosphere or by the nature of the human eye (its optical processing

capabilities), or by both. To the extent that this hypothesis holds, the

moon illusion is an angular size illusion.

Alternatively, we may assume that the moon's perceived angular size

remains constant and it is the human mind (our cognitive apparatus

for reading and interpreting visual signals) which produce the

difference, by computing the distance information contained in the

perceived angular size differently depending on the moon's position in

the sky. To the extent that this hypothesis holds, the moon illusion is a

distance illusion.

Regarding the angular size illusion approach, we can immediately rule out

the "refraction" theory; for although refraction effects do effectively occur,

they again work in the opposite direction: they make the horizon moon look

slightly smaller (by about 1.7%, according to Simanek 2002) and in addition

flatten its shape, thereby making its vertical diameter look even smaller.

Hence, atmospheric refraction effects, far from explaining the moon illusion,

actually imply that the effect that causes the moon illusion is even stronger

than we perceive it. We thus need a refraction-independent explanation of

that unknown effect (or combination of effects). I'll begin with the cognitive

Zenith Moon

Horizon Moon




apparatus (or distance illusion) approach, the so-called sky-dome theory, as it

is the older and still more widely accepted explanation.

The "sky dome" theory This explanation assumes that the perceived

angular size of the moon remains the same, namely, about half a degree. In

agreement with this assumption, we know that high and low moons produce

on the eyes's retina an image of identical size, about 0.15 mm wide. If this

assumption is correct, the only way to explain the apparent variation of size

is that the human mind, dependent on the moon's position above the horizon,

judges its distance differently. We are dealing not with an illusion of angular

size in the first place but rather with an illusion of distance. By analogy, if

two balloons in the sky appear to have the same angular size but we judge

one of them to be further away, the latter will "look" bigger to us. Our mind

recalculates its size, as it were, so as to make up for its increased distance.

But why should our mind do this kind of differential distance computing for

low and high moons, given that we know that the moon is always at the same

distance? The "sky dome" theory explains this by assuming that our mental

model of the sky (and thus, of the moon's orbit), shaped by both our

everyday experience and our theoretical expectations, need not be identical

with the "true" shape of the sky (the moon's actual orbit). Maybe our mental

model of the sky is closer to the ancient view of the sky as a flattened dome

rather than to current astronomical knowledge. In fact this traditional world

view still conforms to a number of everyday experiences: bird watchers, for

example, know that birds flying high are usually closer than those flying near

the horizon. The same holds for airplanes or for clouds.

Our mental model of the sky may also be conditioned by our rather limited

stereoscopic capabilities in judging distance cues. Basically, this conjecture

makes sense because distance cues are not the same at the horizon and at the

zenith. Furthermore, our stereoscopic capabilities have evolved for judging

the distance of near-by objects rather than that of very remote objects in the

sky. Both circumstances may have shaped our mental geometry of visual

space in a way that treats objects above our heads differently from those on

or near the ground.

A lot of sound reasons for taking the sky dome idea seriously! Note,

however, that these reasons alone do not tell us what shape of the sky dome




we should properly assume to help us explain the moon illusion. I find it

rather amazing that all the proponents of this approach of whom I am aware,

have thus far assumed a flat dome model. It seems to me that determining the

precise way in which our mental geometry of visual space differs from

normal geometry is a (possibly complex) question of empirical science rather

than of theoretical speculation only, and thus remains entirely open at

present.

Now, if we do take the idea seriously, it has an important consequence: our

cognitive apparatus then somehow needs to account for the ambiguity of

visual signals about angular size with respect to of distance, perspective, and

linear size. How can it achieve this? Since visual experience is not a reliable

arbiter, it can only assess distance, perspective, and linear size by

recalculating visual signals according to its own inner model of visual space.

Because the process to a large extent occurs unconsciously, what matters is

not so much our contemporary astronomical knowledge (although I would

not preclude that theoretical expectations matter, in as far as they become

intrinsic aspects of our world view) but rather our inner model of the sky

dome, which may differ from one individual to another. If that model,

whether we are aware of it or not, suggests a flat dome, the mind will assume

that low moons are more distant and therefore will make them look larger.

The distance illusion, then, is at heart a sky dome illusion (Figure 1).

Figure 1: Flat sky dome theory of the moon illusionaccording to Kaufman & Kaufman (2000)

Even though the (actual and perceived) angular size of low and high moons

is the same, the distance illusion caused by the mind's flat dome model of the

sky makes it compute different apparent sizes of the moon (black disks).

This, then, is the core thesis of the sky dome theory in its popular flat dome

version.




A modified sky dome theory Thus far, I find the approach rather

illuminating. However, there is a basic difficulty of this explanation: it does

not accurately describe the way most people experience the moon illusion.

For me, at least, it is not true that I perceive low moons to be more distant

than high moons; rather, the contrary is true. In fact, vision researchers have

found that most people judge low moons to be just as close, if not closer than

high moons (see, e.g., Boring 1962 and Gregory 1965). A few authors have

noted this and have concluded that the sky dome theory is altogether

mistaken (e.g. McCready 1965). This conclusion may be too hasty, though:

the experimental finding in question merely implies that the flat sky dome

model is empirically inaccurate, but not that the mental sky model approach

as such is misguided in principle.

It seems too early, then, for throwing the constant angular size hypothesis

definitely over board in favor of the alternative hypothesis, according to

which the moon illusion depends on a changing perception of the moon's

angular size. The empirical fact that the retinal size of the moon does not

differ among low and high moons, along with the mentioned conjectures

concerning our mental geometry of visual space, certainly suggest that the

distance illusion hypothesis has some merits. Hence, before turning to the

angular size illusion hypothesis, it may be worthwhile to consider whether a

modified sky dome model might better describe our experience. To this end,

I suggest to redraw Figure 1 as follows (Figure 2).

Figure 2: Vertical sky dome theory of the moon illusion(describes my personal experience better than

the flat dome model, without claiming to provide a complete explanation)

The modified model according to Figure 2 retains the basic idea that our

mental sky model need not be identical with the true sky, and that the moon

illusion may have something to do with this difference; but it replaces the




experimentally falsified flat dome with a more vertical dome model. I do not

claim that this modified sky dome model provides a valid explanation of the

moon illusion; it is certainly an insufficient, at best partial explanation.

I merely suggest that under the assumption of constant angular size of the

horizon moon as compared to the zenith moon, it corresponds better to the

subjective experience of most people. And since I do not think the current

stage of knowledge allows us to definitively drop the distance illusion

hypothesis in favor of a one-sided angular size illusion hypothesis, it

certainly makes sense to try to save the sky dome model from its overt

inconsistency with the actual experience of a majority of observers.

Whether or not the constant angular size assumption is adequate, and what

are its theoretical merits as compared to the angular size illusion approach,

cannot be decided on the basis of the model itself but requires extensive

empirical research. All that the modified model aims to suggest is that it is

possible to reconcile the constant angular size hypothesis with the empirical

finding that most people see the horizon moon closer than the zenith moon, a

finding that is inconsistent with the conventional flat dome model usually

associated with the constant angular size assumption.

As a welcome side-effect, the modification also responds to the fact that the

ancient flat dome concept of the sky has longs since been replaced by a

different view of the cosmos. Our notion of the nightly sky is no longer

shaped by a flat horizon of expectations, to use Karl R. Popper's (1972, p.

345) pertinent phrase for describing the theory-impregnated character of all

human experience. Nowadays, when we raise our eyes to the zenith, we

imagine not a flat dome but rather, infinite space. (On the other hand, when

we turn our eyes back to the ground, our visual horizon tends to be more

limited than in earlier centuries, whether by the next group of ugly buildings

or by polluted atmospheric conditions.) A vertical sky dome model certainly

captures our contemporary mind set as well as the ancient flat dome concept.

Furthermore, I would suggest that the revised sky dome model may, but need

not, assume that the perceived angular size of the moon indeed remains

constant. This is, in fact, another unnecessary assumption; it suffices to

assume that the constant angular size assumption has some part to play in

putting together the unsolved puzzle. I see no reason why an adequately




calibrated sky dome model might not contribute to understanding the moon

illusion even if it should turn out in the end that the constant angular size

hypothesis cannot be upheld. Considering the role of our mental sky model –

our horizon of expectations, as it were – may be just as meaningful in

combination with the angular size variation hypothesis. Given the magnitude

of the moon illusion, it seems not implausible that both effects, a distance

illusion and an angular size illusion, are needed to explain the full extent of

the moon illusion.

The "oculomotor micropsia" theory Let us, then, turn to this second of

the earlier-mentioned basic hypotheses and assume that the perceived

angular size of the moon varies with its position in the sky. To the extent that

this assumption holds, we can and need not (at least not fully) explain the

moon illusion by the role of an inaccurate mental sky model and by the

illusion of varying distance that it causes; rather, we then primarily need to

look at the visual processing capabilities of our eye.

Among the main proponents of this approach are McCready (1965, 1986,

2004), Enright (1989a, b), and Roscoe (1989). We need not know the details

of their theory in order to understand the basic idea. It says that the perceived

angular size of an object varies with the focal distance of our eyes. This is an

experimental finding that you can approximately simulate in the following

way. Watching your computer monitor, hold a small object such as a pen

about 20 cm away from your eyes in front of the monitor. Now focus your

eyes on the pen and watch what happens to the monitor – it looks smaller. It

has changed its angular size!

There is thus an obvious connection between the focal point of our

stereoscopic vision – the accommodation of the eye lenses and the

simultaneous convergence of the eyes to a certain distance – and the

perceived angular size of objects. The exact nature of the connection is

complex and requires more research, but basically we can say that the closer

our focal point is, the smaller look more distant objects. This is what vision

researchers call oculomotor micropsia, an effect that probably results from a

combination of both accommodative micropsia (reduction in angular size

caused by increased accommodation) and convergence micropsia (reduction

in angular size caused by increased convergence of the eyes). Micropsia is a




Greek noun meaning "small sight" or "small appearance" in the sense of a

smaller-than-real illusion. The effect was first described by the English

physicist Sir Charles Wheatstone (1872), the inventor of the stereoscope (a

device that generates a three- dimensional view from two photographs of the

same subject taken at slightly different angles). The reverse effect is called

macroscopia; it occurs when our focal point is more distant than an object,

and has us see the object bigger than we'd expect.

Enright (1989a, b) and Roscoe (1989) have demonstrated these effects

experimentally. More recent research indicates that micropsia and macropsia

may equally occur when eye lens muscles are paralyzed or absent, or when

one eye is covered. Obviously, the two effects are controlled by neurological

processes (the same ones that control the eye movements) rather than

directly and only by the mechanics of the eye movements themselves; let us

not misunderstand the name "oculomotor micropsia / macropsia" in this

respect. The fact that angular size illusion can be produced experimentally by

influencing the movements (accommodation and convergence) of the eyes

need not mean this is the only way such illusions can arise. Lest we make

unnecessary assumptions, let us consider micropsia and macropsia as

primarily but not exclusively occurring at the level of perception, and keep in

mind the role of the brain in processing all visual signals.

Applied to the moon illusion, the theory postulates that the zenith moon

looks smaller, and consequently more distant. One possible explanation is

the earlier-mentioned difference of available distance cues near the horizon

and near the zenith. Near the horizon, we usually can rely on familiar

distance cues such as houses, trees, mountains and so on, which help our

eyes to focus on a point that is more remote than these objects. Near the

zenith, however, no such cues are available to direct our stereoscopic vision.

Experimental findings show that in the absence of distance cues, our eyes

tend to focus on a default focal point – its resting focus – which is much

closer than the moon's actual distance. Leibowitz et al. (1975) have found it

to be some 2 m away only. Vision researchers speak of an empty field

micropsia. Now take our previous little experiment and substitute the zenith

moon for the computer monitor: since the default focus is much closer to

your eyes than the moon's actual distance, you perceive the zenith moon as

smaller than you would otherwise; and since your focal point is also closer




than the horizon where you watch the rising moon, the zenith moon looks

smaller than the horizon moon, and vice-versa. The earlier-mentioned

evolutionary difference between our capabilities of handling horizontal and

vertical distances may also be part of the explanation. Finally, darkness may

also induce micropsia, for obvious reasons: it renders the use of distance

cues more difficult. Vision researchers speak of night micropsia.

In conclusion Despite many open questions, it appears safe to say that the

following aspects play a major role in the moon illusion:

Shortcomings of our stereoscopic vision in dealing with large

distances: Our stereoscopic capabilities are not made for visual objects

more than a few hundred meters away.

Shortcomings of our mental processing of visual signals coming from

above the head: Evolutionary conjectures suggest we do not handle

such signals as well as signals coming from the ground.

Complex interdependence of perception and cognition: The processing

of visual signals moves at different, partly unconscious levels that

interact in complex ways. In order to translate the visual signals

received by the retina into geometric interpretations of the location and

movement of objects in space, we depend on a (partly unconscious)

inner mental model of visual space.

Shortcomings of our mental geometry of visual space: Our mental

model of visual space need not (and probably cannot) be the same as

the "true" geometry of space (assumed versus "true" sky dome).

Importance of distance cues: For all the previous phenomena, our

handling of distance cues – or their absence – appears to play a crucial

trigger role.

Inseparability of size and distance illusions: All the mentioned

difficulties of processing stereoscopic spatial information can be

understood to cause either illusions of distance (sky dome theory) or

illusions of size (oculomotor theory), or both. Since angular size and

distance are interdependent, it seems plausible to assume that both

kinds of illusions work together in causing the moon illusion.




Magnitude of the moon illusion as compared to the effects explained

by any available explanation: The last-mentioned conclusion is

supported by empirical findings which suggest that angular size

illusions or distance illusions alone do not produce effects nearly as

large as the moon illusion. The micropsia / macropsia theory, for

instance, accounts experimentally for angular size differences of less

than 10% (Simanek 2002), while the perceived angular size difference

of the horizon moon as compared to the zenith moon is around 50%.

It cannot surprise, then, that recent reviews of the moon illusion literature

(Ross and Plug 2002, Simanek 2002) conclude that no single theory

available today can really explain the mystery. For the time being, the moon

keeps its secret.

Some doubts and philosophical issues As convincing as both basic

approaches to explaining the moon illusion may appear at first, it soon

becomes obvious that neither looks at the whole picture:

Theoretically speaking, both theories look too simple to me. The sky

dome theory appears too simple because it one-sidedly focuses on our

cognitive apparatus, at the cost of rather neglecting the primary

difficulties at the level of perception itself. The oculomotor theory, on

the other hand, appears equally one-sided in seeking the explanation in

the limitations of our stereoscopic vision, while rather neglecting the

way our cognitive apparatus may have learned to handle some of the

limitations.

Empirically speaking, neither approach is currently able to account for

more than a fraction of the full extent of the moon illusion.

Both theoretically and empirically, the complementary nature of the two

explanatory approaches seems therefore rather obvious, even though the

involved researchers tend to treat them as mutually incompatible. I certainly

recognize the difficulties that researchers may face in combining them, but

even so, I see no intrinsic reasons why neither side should be able to

integrate what the other side has to contribute.

Rather, it's probably just not the way science works. Researchers are eager to




uncover the weaknesses rather than the merits of competing approaches. It

seems to me that in the case of the moon illusion, the two competing

approaches are involved in a sort of (unnecessary) paradigm war. Every war

has victims; in this case it is the fundamental interdependence of perceptual

and cognitive phenomena which somehow seems to have got out of focus. At

least this is the impression conveyed to me by the two main sources that I

have consulted, by authors who are major contemporary representatives of

the two approaches: Kaufman & Kaufman (2000) for the sky dome

paradigm, who seek the root cause of the moon illusion in a distance illusion,

and McCready (2004) for the oculomotor paradigm, who seeks the root

cause in an angular size illusion. I could not help but gain the impression that

both articles are more concerned to argue why the other side has got it wrong

than to support the competing theory with their own specific insights.

Apart from this general doubt concerning the isolationist tendencies of both

sides, I have, of course, a number of more specific doubts. I find it difficult

to understand, for instance, how the protagonists of the oculomotor

microscopia /macroscopia theory can assume that the perceived angular size

of the moon varies with the position of the moon in the sky, without carefully

discussing the contrary experimental findings which suggest that the moon

image on the retina has a constant size of about 0.15 mm in diameter. The

theory thus in effect assumes what it proposes to explain, namely, deception.

Secondly, the theory depends on assuming persistent visual deception. I miss

an explanation of this persistent nature of the deception, that is, of the

apparent absence of learning. It makes sense to assume that children easily

take micropsia or macropsia effects for granted – need I refer to Gulliver in

Lilliput or to Alice in Wonderland? However, once we are adults, shouldn't

we expect that over time, we will learn to focus more correctly, given that we

know we are victims of a visual illusion? Why is there apparently no

learning? Why does the theory tell us so little about this question? Is it

perhaps because obviously, considering the role of learning means giving

more weight to what happens at the cognitive level, the territory of the rival

theory?

But of course, a similar doubt can be formulated against the sky dome

theory. Once we are conscious of the difference between our inner mental




sky and the true outer sky, shouldn't we expect that we can eventually adapt

our inner model so as to avoid obvious deception? Actually, when we pass

from childhood to adulthood, some learning does seem to occur, as

Leibowitz and Hartman (1959) report, but this apparently does not manage to

match the full extent of the moon illusion.

In other words, the current state of research into the moon illusion leaves me

with more questions than answers. For example, can persistently wrong eye

convergence and accommodation (the hypothesis of a basic angular size

illusion at the level of perception) really explain the full extent of the moon

illusion? Hardly. Likewise, can a persistently inaccurate mental model of the

sky (the hypothesis of constant angular size, with its implication of a

distance illusion at the cognitive level) fully explain it? Hardly. Can the

limitations of our stereoscopic capabilities in dealing with distant objects,

which is a core issue of both approaches, really be explained by

concentrating either on perceptive (optical) or on cognitive (mental)

processes? Hardly. And so on. There is no way round it: the state of our

knowledge about the moon illusion is hardly satisfactory.

Although this state of affairs certainly does not cause me sleepless nights,

epistemologically speaking I find it thought provoking. If this is how science

fails to explain a familiar everyday phenomenon in the sky, can we imagine

how it must fail to do justice to more complex and less obvious issues? The

unsolved mystery of the moon illusion thus at least helps us in avoiding

another persistent illusion, that of the "secure path" (Kant 1781) and

objective nature (Popper 1972) of science. The moon illusion as an

epistemological warning signal, as it were! If we take it seriously, it invites

philosophical reflection on our possibly distorted "horizon of

expectations" (or should I say: mental model?) regarding science. I would

like to conclude by hinting at just three possible reflections.

Socrates and science: If science is unable thus far to elucidate and

explain even an everyday empirical phenomenon such as the moon

illusion, perhaps we should remind ourselves more than currently en

vogue of the virtue of Socratic modesty in science? Could a more

Socratic practice of science not have benefited moon illusion research,

for example, by helping oculomotor and sky dome protagonists avoid




all-too one-sided claims in favor of more cooperation and multi-

dimensional theorizing?

Constructivism, nothing new under the sun: At least since Kant's

"Copernican turn" away from naive realism to critical idealism, we

know that we tend to see what we expect; that all knowledge is

individually and socially constructed. Despite much fashionable talk

about constructivism, critical realism, and other supposed

epistemological insights of our time, Kant has given us the basic

critical message long ago: "To avoid errors, one must search for their

origin in illusion. Uncovering illusion is a much greater service to truth

than any direct refutation of errors.” (my transl. from Vorlesungen

über die Logik, see Kant 1992). Should moon illusion research perhaps

be taken much more seriously than it has been taken thus far, both

scientifically and epistemologically?

Popper's horizon of expectations, turned critically: Popper's insights

into the epistemological importance of our theoretical horizon of

expectations are rarely matched by similar lucidity about the

importance of two other major factors that condition all our knowledge

claims, namely, value judgments and boundary judgments. In my work

on critical systems heuristics, I have attempted to provide a generic

framework for boundary critique in contexts of applied science and

professional practice, because boundary judgments underpin all our

judgments of what are relevant facts and values. Could there perhaps

be an equivalent critical heuristics for basic science?

And finally: what kind of a world would it be in which the failure of moon

illusion research would be taken seriously?

References

Boring, E.G. (1962). On the moon illusion. Science, 137, 902-906.

Enright, J.T. (1989a). The eye, the brain and the size of the moon: toward a unified oculomotor hypothesis for the moon illusion. In M. Hershenson (ed.), The Moon Illusion,Hillsdale, NJ: L. Earlbaum, Chapter 4, 59-121.

Enright, J.T. (1989b). Manipulating stereopsis and vergence in an outdoor setting : Moon, sky and horizon. Vision Research, 29, No. 12, 1815-1824.

Gregory, R.L. (1965b). Seeing in depth. Nature, 207, 16-19.

Kant, I. (1781). Critique of Pure Reason, transl. by N.K. Smith. New York: St. Martin's Press 1965.




Kant, I. (1992) Lectures on Logic. The Cambridge Edition of the Works of Immanuel Kant in Translation, Cambridge, UK: Cambridge University Press 1992 German orig. 1800).

Kaufman, L., and Kaufman, J.H. (2000). Explaining the moon illusion. Proceedings of the National Academy of Sciences of the United States of America, 97, No. 1 (January 4), 500-504.

Leibowitz, H., and Hartman, T. (1959). Magnitude of the moon illusion as a function of the age of the observer. Science, 130, 569-570.

Leibowitz, H., Hennesy, R.T. and Owens, D.A. (1975). Intermediate resting position of accommodation and some implications for space perception. Psychologia, 18, No. 3, 162-170.

McCready, D. (1965). Size-distance perception and accommodation- convergence micropsia: a critique. Vision Research, 5, 189-206.

McCready, D. (1986). Moon illusions redescribed, Perception & Psychophysics, 39, No. 1, 64-72

McCready, D. (2004). The moon illusion explained. Web publication, first published 7 December 2002, revised 10 November 2004, available at http://facstaff.uww.edu/mccreadd/index.html .

Popper, K.R. (1972). Objective Knowledge: An Evolutionary Approach. Oxford, UK: Clarendon Press.

Roscoe, S.N. (1989). The zoom-lens hypothesis. In M. Hershenson (ed.), The Moon Illusion,Hillsdale, NJ: L. Earlbaum, Chapter 3, 31-57.

Ross, H., and Plug, C. (2002). The Mystery of the Moon Illusion. Oxford, UK: Oxford University Press.

Simanek, D.E. (2002). The moon illusion, an unsolved mystery. Web publication, revised 11 January 2002 (original publication date not given), available at http://www.lhup.edu/%7Edsimanek/3d/moonillu.htm .

Wheatstone, C (1852). Contributions to the physiology of vision, Part 2. Philosophical Transactions of the Royal Society, Part 2, 1-17.

Technical data Digital photograph taken on 26 June 2004 around

9:30 p.m., shutter speed 1/60, aperture f/2.8, ISO 50, focal length 8 mm

(equivalent to 36 mm with a conventional 35 mm camera). Original

resolution 1158 x 759 pixels; current resolution 1255 x 764 pixels,

compressed to 45 KB.

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July, 2005



http://facstaff.uww.edu/mccreadd/index.html

http://www.lhup.edu/


„The sky's the limit”(An insight that certainly applies to our limited understanding of the moon illusion)

A case of micropsia? Summer moon rising into the evening sky

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Last updated 6 Dec 2009 (layout) and 3 July 2005 (text, first published 1 July 2005)


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